7. A force stretches a wire by 1 mm. a. A second wire of the same material has the same cross section and twice the length. How far will it be stretched by the same force? Explain. b. A third wire of the same material has the same length and twice the diameter as the first. How far will it be stretched by the same force? Explain.

(a) The second wire will be stretched by 2 mm

(b) The third wire will be stretched by 0.25 mm

Explanation:

Tensile stress on every engineering material is given as the ratio of applied force to unit area of the material.

σ = F / A

Tensile strain on every engineering material is given as the ratio of extension of the material to the original length

δ = e / L

The ratio of tensile stress to tensile strain is known as Young's modulus of the material.

Part A

cross sectional area and applied force are the same as the original but the length is doubled

The second wire will be stretched by 2 mm

Part B

a third wire with the same length but twice the diameter of the first

e₁ = ¹/₄ x 1 mm = 0.25 mm

The third wire will be stretched by 0.25 mm